# Appendix D – Sourcing mechanism in the PE-CGE model

The following equations and diagram show a series of nests indicating the various substitution possibilities allowed by the PE-CGE model to represent the inter-regional trade structure. We used the trade margin technological change variable to show the impact of improvements in road transport margin on the economy.

Equation (1):

\begin{aligned} &XTRADMAR(c,s,m,r,d) = \nonumber \\ & ATRADMAR(c,s,m,r,d)*XTRAD(c,s,r,d) \end{aligned}

Equation (2):

\begin{aligned} &PDELIVRD(c,s,r,d)*XTRAD(c,s,r,d) = \\ & PBASIC(c,s,r)*XTRAD(c,s,r,d)+ \\ & \sum\left(m,MAR, PSUPPMAR_{P(m,r,d)}*XTRADMAR(c,s,m,r,d)\right ) \\ \end{aligned}
 ATRADMAR(c,s,m,r,d) Trade for margins technological change XTRAD(c,s,r,d) Quantity of good c,s from r to d XTRADMAR(c,s,m,r,d) Margin m on good c,s going from r to d PBASIC(c,s,r) Basic prices PDELIVRD(c,s,r,d) All-user delivered price of good c,s from r to d XSUPPMAR_P(m,r,d) Quantity of composite margin m on goods from r to d PSUPPMAR_P(m,r,d) Price of composite margin m on goods from r to d

Source: Horridge and Pearson (2011); Principal Economics